The present invention relates to an educational device or toy, particularly useful in teaching a number system, particularly the base 10 number system, to people, particularly children.
The base 10 number system contains only four concepts: the use of the digits 0-9; the idea of place, that is, as you move one place to the left a digit is ten times the value of the same digit one place to the right; the concept of zero, that is, a valueless, but very meaningful place holder; and finally, the most difficult, that is, the concept of the "tens changing process" (regrouping as taught in first grade beginning approximately in 1960). In the "tens changing process", when 10 units are accumulated in any one given place, they are evenly exchanged for one unit in the next higher place. Ten 1's are exchanged for one 10; ten 10's are exchanged for one 100, etc.
The above four concepts serve only to make manipulation of numbers easier although most five to nine year olds wouldn't agree nor would their parents struggling over their childrens' "new math" text. The usefulness of these concepts and how they relate can be illustrated with the following story.
Long ago, in ancient Babylon, there lived a wise and very wealthy shepherd named Count Tenio. He kept count of his huge herd of sheep by putting a pebble in a large urn each time a lamb was born or bought and removed a pebble from the urn when one of his sheep died. But, although he knew he had a gigantic herd he couldn't tell exactly how many sheep there were because he couldn't count--the number system hadn't been invented.
Soon, Count Tenio suspected that his helpers were stealing sheep from him--just a few at a time but he couldn't say for sure because he really didn't know how many sheep he had. That urn of pebbles wasn't helpful either; although he knew there were many pebbles, he couldn't count them.
He decided he would sue his helpers in a court of law. But they and he knew he would lose his case, because he had no evidence of exactly how many sheep he had. Count Tenio solved his problem--he invented the number system. He still used pebbles but this time not so many.
That night while his sheep slept he stole into the barn and this is what he did. He lined up five urns and he started filling them with pebbles, one for each sheep, only no urn contained more than his fingers worth of pebbles--each time he reached his fingers worth he exchanged all the pebbles for one pebble which he put in the urn to the left. When that urn had his fingers worth of pebbles he took them all out and put one pebble in the next urn to the left.
At this point, he realized he had better label those urns so everyone would understand what they meant. The urn on the far right had the least value--each pebble stood for only one sheep--this he called the ones' urn. In the urn to the left of the ones' urn each pebble stood for his fingers worth of sheep or one pebble in this urn stood for the whole ones' urn. He called this the tens' urn. In the urn to the left of the tens' urn each pebble was worth one tens pebble; this he called the hundreds' urn. And finally, the urn to the left of the hundreds' urn was the thousands' urn; each pebble in the thousands' urn was equal to his fingers worth of pebbles in the hundreds' urn.
Next he decided that his fingers worth was too inexact; he needed something to stand for each finger so he designed numerals to stand for each finger; 1, 2, 3, 4, 5, 6, 7, 8, 9. Since all his fingers would be equal to one pebble in the next left urn he let that be a 1 again but put a 0 to the right of it to show everyone that pebble was in the tens' urn--the one to the left of the ones' urn. The 0 stood for an empty urn but showed that in a number system that relies on place an empty urn is just as important as one with a pebble in it. The hundreds' urn had a 1 for the pebble in the hundreds' urn and a 0 for no pebbles in the tens' urn and 0 for no pebbles in the ones' urn. With those two 0's everyone would know where that one pebble was. Zeros as place holders would enable him to show a difference between one sheep and many by just using one pebble.
That first night Count Tenio counted 6 thousands, 8 hundreds, 4 tens and 7 ones sheep. He didn't tell anyone about his new counting method. The next night using his new system he counted again. Aha! He was right--this time he had 6 thousands, 8 hundreds, 4 tens and 1 sheep. Six sheep had been stolen. Just as he suspected. The following night his count came to 6 thousands, 8 hundreds, 3 tens and 2 ones sheep. Altogether 1 tens and 5 ones worth of sheep had been stolen (we would say 15). With the old method he never would have detected his loss, but now he knew for sure.
The following day he went to court and won his case. The three thieves said they thought he'd never be able to count the missing sheep.
Not only did the shepherd win his case, but for the rest of time Count Tenio's number system, the base 10 number system, has been used by mankind to keep track of numbers of things.
U.S. Pat. No. 3,455,033, to Bing-Hou Han, discloses an educational device, which is useful in teaching the number system. A ball calculator employs upper and lower registers with ten keys as shown in FIG. 11, which control the flow of marbles through the channels. Carrying can be employed, for example when adding.
U.S. Pat. No. 2,463,763 to Graff shows a ball computing apparatus which teaches the idea of carrying, but the carrying is done manually rather than automatically. Different colored balls are used to show the need for carrying.
The above two devices, while useful, are difficult to use and require considerable explanation as to their proper use, which seriously hinders their use in teaching children or others unfamiliar with the number system.
U.S. Pat. No. 3,908,287 to Darnell is a visual aid in teaching mathematics, but is not easily understood by beginning students and not sufficiently interesting to hold the attention span of children for very long.